Kernel machines as well as neural networks possess universal function approximation properties. Nevertheless in practice their ways of choosing the appropriate function class differ. Specifically neural networks learn a representation by adapting their basis functions to the data and the task at hand, while kernel methods typically use a basis that is not adapted during training. In this work, we contrast random features of approximated kernel machines with learned features of neural networks. Our analysis reveals how these random and adaptive basis functions affect the quality of learning. Furthermore, we present basis adaptation schemes that allow for a more compact representation, while retaining the generalization properties of kernel machines.

Curt Cignetti was so focused this offseason, he turned down all external requests: 'I'm 95% football' Former MLB owner claims'despicable' San Francisco Giants are the reason the A's left Oakland Longtime NASCAR crew chief tells wild story about one of the sport's biggest characters WNBA finally embraces Caitlin Clark's stardom with unprecedented national TV schedule Why are the Mets so bad? Flyers mascot Gritty pens letter to fans ahead of first playoff game... eight years after he debuted NFL Draft prospect Rueben Bain Jr. mum about 2024 crash when publicly asked about it for first time Troy Aikman is selling'fire suites,' which are exactly what they sound like Fernando Mendoza's first pitch at Marlins game draws harsh reviews Steve Hilton praised for'offering solutions' in CA gubernatorial debate Middle East tensions escalate over US blockade, Iran's actions Michael Easter and Gary Brecka discuss the'choice' to live to be 100 Sen Ted Cruz calls new deadline with Iran'really consequential' RFK Jr confronted over'raccoon parts' on Capitol Hill Our democracy is not'in crisis,' Sen John Fetterman says The DOJ is'on the offense' here, Andrew Kolvet says OutKick ChatGPT predicted the first round of the NFL Draft and here's what it said Ultimate human vs. machine showdown as OutKick's Dan Z. takes on ChatGPT in a mock draft battle Where Is The Value In This NFL Draft? Jonathan Hutton & Chad Withrow ask Armando Salguero what position has the most value in this year's NFL draft I'm not sure why I do these things to myself, but I decided to go head-to-head with ChatGPT in a mock draft competition. I recently released my final mock draft, and then I asked ChatGPT to predict the entire first round. Below, you will see where we are the same and where we are different.

Deep learning methods achieve state-of-the-art performance in many application scenarios. Yet, these methods require a significant amount of hyperparameters tuning in order to achieve the best results. In particular, tuning the learning rates in the stochastic optimization process is still one of the main bottlenecks. In this paper, we propose a new stochastic gradient descent procedure for deep networks that does not require any learning rate setting. Contrary to previous methods, we do not adapt the learning rates nor we make use of the assumed curvature of the objective function. Instead, we reduce the optimization process to a game of betting on a coin and propose a learning rate free optimal algorithm for this scenario. Theoretical convergence is proven for convex and quasi-convex functions and empirical evidence shows the advantage of our algorithm over popular stochastic gradient algorithms.

We introduce and study the problem of calibrating conditional risk, which involves estimating the expected loss of a prediction model conditional on input features. We analyze this problem in both classification and regression settings and show that it is fundamentally equivalent to a standard regression task. For classification settings, we further establish a connection between conditional risk calibration and individual/conditional probability calibration, and develop theoretical insights for the performance metric. This reveals that while conditional risk calibration is related to existing uncertainty quantification problems, it remains a distinct and standalone machine learning problem. Empirically, we validate our theoretical findings and demonstrate the practical implications of conditional risk calibration in the learning to defer (L2D) framework. Our systematic experiments provide both qualitative and quantitative assessments, offering guidance for future research in uncertainty-aware decision-making.

Forecasting the life-cycle trajectory of a newly launched product is important for launch planning, resource allocation, and early risk assessment. This task is especially difficult in the pre-launch and early post-launch phases, when product-specific outcome history is limited or unavailable, creating a cold-start problem. In these phases, firms must make decisions before demand patterns become reliably observable, while early signals are often sparse, noisy, and unstable We propose the Conditional Diffusion Life-cycle Forecaster (CDLF), a conditional generative framework for forecasting new-product life-cycle trajectories under cold start. CDLF combines three sources of information: static descriptors, reference trajectories from similar products, and newly arriving observations when available. Here, static descriptors refer to structured pre-launch characteristics of the product, such as category, price tier, brand or organization identity, scale, and access conditions. This structure allows the model to condition forecasts on relevant product context and to update them adaptively over time without retraining, yielding flexible multi-modal predictive distributions under extreme data scarcity. The method satisfies consistency with a horizon-uniform distributional error bound for recursive generation. Across studies on Intel microprocessor stock keeping unit (SKU) life cycles and the platform-mediated adoption of open large language model repositories, CDLF delivers more accurate point forecasts and higher-quality probabilistic forecasts than classical diffusion models, Bayesian updating approaches, and other state-of-the-art machine-learning baselines.

Looking for a better way to pinpoint the precise LEGO bricks he needed, a tech writer turned to OpenAI’s Codex for help.

The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model. However, the key challenge in GPSSMs has not been satisfactorily addressed yet: system identification, i.e., learning the model. To address this challenge, we impose a structured Gaussian variational posterior distribution over the latent states, which is parameterised by a recognition model in the form of a bi-directional recurrent neural network. Inference with this structure allows us to recover a posterior smoothed over sequences of data. We provide a practical algorithm for efficiently computing a lower bound on the marginal likelihood using the reparameterisation trick. This further allows for the use of arbitrary kernels within the GPSSM. We demonstrate that the learnt GPSSM can efficiently generate plausible future trajectories of the identified system after only observing a small number of episodes from the true system.

This study deals with neural networks in the sense of geometric transformations acting on the coordinate representation of the underlying data manifold which the data is sampled from. It forms part of an attempt to construct a formalized general theory of neural networks in the setting of Riemannian geometry. From this perspective, the following theoretical results are developed and proven for feedforward networks. First it is shown that residual neural networks are nite dierence approximations to dynamical systems of rst order dierential equations, as opposed to ordinary networks that are static. This implies that the network is learning systems of dierential equations governing the coordinate transformations that represent the data. Second it is shown that a closed form solution of the metric tensor on the underlying data manifold can be found by backpropagating the coordinate representations learned by the neural network itself. This is formulated in a formal abstract sense as a sequence of Lie group actions on the metric bre space in the principal and associated bundles on the data manifold. Toy experiments were run to conrm parts of the proposed theory, as well as to provide intuitions as to how neural networks operate on data.

One group of hackers used AI for everything from vibe coding their malware to creating fake company websites--and stole as much as $12 million in three months. The advent of AI hacking tools has raised fears of a near future in which anyone can use automated tools to dig up exploitable vulnerabilities in any piece of software, like a kind of digital intrusion superpower. Here in the present, however, AI seems to be playing a more mundane, if still concerning, role in hackers' toolkit: It's helping mediocre hackers level up and carry out broad, effective malware campaigns. That includes one group of relatively unskilled North Korean cybercriminals who've been discovered using AI to carry out virtually every part of an operation that hacked thousands of victims to steal their cryptocurrency. On Wednesday, cybersecurity firm Expel revealed what it describes as a North Korean state-sponsored cybercrime operation that installed credential-stealing malware on more than 2,000 computers, specifically targeting the machines of developers working on small cryptocurrency launches, NFT creation, and Web3 projects.